Question : a and b are two positive integers such that the least prime factor of a is 3 and the least prime factor of b is 5. Then calculate the least prime factor of (a+b).
Doubt by Muskan
OR
Question : a and b are two positive integers such that least prime factor of a is 3 and the least prime factor of b is 5. Then, the least prime factor of (a+b) is
a) 2
b) 3
c) 5
d) 8
Doubt by Vanshika
Solution :
Least prime factor of 'a' is 3 (Given)
⇒ a is not the prime factor of 2.
⇒ a must be an odd number.
Least Prime factor of 'b' is 5 (Given)
⇒ a is not the prime factor of 2.
⇒ a must be an odd number.
Now when we add both 'a' and 'b' then we get an even number.
[ ∵From the basic concepts of numbers, we know that the sum of two odd numbers always gives an even number]
⇒ (a+b) must be an even number.
We know, every even number is divisible by 2 or we can say that (a+b) must have 2 as a prime factor.
∵ 2 is already the least prime number. So we can say that the least prime factor of (a+b) is 2.
Hence, a) 2, is the correct option.
Similar Question : If 3 is the least prime factor of number 'a' and 7 is the least prime factor of number 'b', then the least prime factor of (a+b) is
a) 2
b) 3
c) 5
d) 10
Doubt by Saumya
Ans : a) 2